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Nearly two decades of reverberation mapping (RM) studies on nearby AGN have revealed a tight correlation between the size of the Hbeta broad-line region and the optical luminosity of the AGN comma designated the R-L relation. This correlation is the foundation for the so-called d_commasingle-epoch virial black hole mass estimatorsd_comma that have been widely applied to distant quasars to estimate their black hole masses without dedicated RM measurements. Recent RM measurements for quasars beyond the nearby Universe and for a subset of nearby AGN with estimated high accretion rates have independently revealed a systematic offset from the canonical R-L relation based on the nearby RM AGN sample. The most likely explanation of this offset is that these new RM samples explore AGN that have different accretion rates and therefore different shapes of the continuum spectral energy distribution (SED) comma responsible for ionizing the line-emitting gas comma than the nearby RM AGN sample. We propose STIS UV spectroscopy for a sample of 18 quasars at zvirgul0.4 from one of these recent RM samples to test this hypothesis and to develop empirical corrections to the R-L relation based on additional AGN parameters. We will model the UV spectra with detailed photoionization calculations to constrain the ionizing continuum directly incident on the broad-line region gas. The combination of UV and (existing) optical spectroscopy for a unique non-local AGN sample with direct RM-based black hole masses also will enable better SED-fitting to constrain accretion parameters and better calibrations of single-epoch mass recipes based on UV broad emission lines.